AFM cantilevers and methods for making and using same

ABSTRACT

The invention provides high performance cantilevers with optimal combinations of high resonant frequency and low force constant. In one aspect, AFM cantilevers with spring constants in the range 1-10 −6  N/m with (fundamental) resonant frequencies in aqueous solutions of 0.1-100 MHz are provided. A high performance cantilever may be made by focused ion beam milling or electron deposition. The high performance cantilevers allow faster scanning, increase the temporal resolution of force measurement, improve measurement sensitivity by reducing cantilever noise, and improve sensitivity by reducing cantilever spring constant.

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Application 60/280,267, filed Mar. 30, 2001 and to U.S.Provisional Application No. 60/314,235, filed Aug. 22, 2001, theentireties of which are incorporated by reference herein.

FIELD OF THE INVENTION

The invention relates to high performance cantilevers for scanning probemicroscopes, such as Atomic Force Microscopes, and to methods of makingand using the same.

BACKGROUND OF THE INVENTION

Scanning probe microscopes (SPMs) obtain data regarding surfacetopography by using a sharp tip or probe on the end of a cantilever heldon or at a short distance (e.g., about 5-500 Å) from a sample. Thecantilever tip can be deflected by various forces acting at theinterface between the sample and the tip, such as electrostatic,magnetic, and van der Waals forces. A movement of the cantilever due tointeractions between an atom at the end of the tip and an atom of thesample can then be measured electrically (as in a Scanning TunnelingMicroscope, or STM) or optically (as in an Atomic Force Microscope, orAFM). By scanning the sample in x- and y-directions to change itsposition relative to the cantilever tip, three-dimensional informationregarding the surface features of a sample can be obtained (see, e.g.,Binnig, et al, 1986, Phys. Rev. Lett. 56(9): 930-933); McClelland, etal., 1987, Rev. Progr. Quart. Non-Destr. Eval. 6: 1307; Martin, et al,1987, J. Appl. Phys. 61(10): 4723-4729).

AFM cantilevers operate in an oscillating mode or in a non-oscillatingmode and can further interact with a sample in a contact mode or in anon-contact mode. In an oscillating contact mode, the cantilever isoscillated mechanically at or near its resonant frequency so that itstip repeatedly taps a sample surface, thus reducing the tip'soscillation amplitude. In an oscillating non-contact mode, interactionsbetween the sample and the tip alter the tip's oscillation amplitude orfrequency. The change in oscillation amplitude indicates proximity tothe sample surface and may be used as a signal for feedback (e.g., forcontrol of probe scanning). In a non-oscillating contact mode, thecantilever is not oscillated, and cantilever deflection is monitored asthe tip is dragged over the sample surface, while in a non-oscillatingnon-contact mode, attractive interactions between the tip and the sampleshift the cantilever resonance frequency.

Atomic force microscopy is emerging as an important tool in methodswhich rely on detecting information about surface features of a sample,measuring forces between two surfaces, or fabricating nanostructures(e.g., on silicon wafers, thin film magnetic read/write heads, and thelike) (see, e.g., U.S. Pat. No. 6,337,479).

Atomic force microscopy also has many applications in biomedicalresearch. It can be used for high contrast, high resolution imaging ofbiological surfaces in a wide range of environments (Engel, et al.,1999, Trends Cell Biol. 9: 77-80; Czajkowsky and Shao, 1998, FEBS Lett.430: 51-4. 1998; Bustamante, et al., 1997, Curr. Opin. Struc. Biol. 7:709-16; Hansma and Hoh, 1994, Ann. Rev. Biophys. Biomol. Struct. 23:115-39.) It also can be used to measure intermolecular forces (e.g.,Heinz and Hoh; 1999, Trends Biotech. 17:143-150; Mann, S. and H. E.Gaub, 1997, Curr. Opin. Colloid Interface Sci. 2: 145-152; Cappella andDietler, 1999, Surf. Sci. Rep. 34: 1), intramolecular forces (Lee, etal., 1994; Lee, et al., 1994, Science 266: 771-773. 1994; Rief, et al.,1997, Science 275: 1295-7), and local mechanical properties (A-Hassan etal., 1998, Biophys. J. 74: 1564-1578; Vinckier and Semenza, 1998, FEBSLett. 430: 12-6. 1998; Radmacher, et al., 1996, Biophys. J. 70:556-567). Imaging with AFM offers advantages for studying biologicalsamples, because the samples do not require drying, sectioning, metalcoating or chemical fixing prior to analysis. Thus, AFMs may be usedwith samples that require very little sample preparation, includingsamples that are biologically active in both ambient air (includingdried samples) and liquid.

One of the limiting elements in current AFMs is the design of thecantilever. The performance of the cantilever is primarily constrainedby a combination of its fundamental resonant frequency (ω) and springconstant (k). Typical cantilevers of the prior art are on the order of85-500 μm long and have resonant frequencies substantially less than 500KHz. For example, generally, prior art cantilevers have lengths on theorder of 85-320 μm, widths of 10-20 μm and thicknesses on the order of0.5 μm. This produces typical [k, ω_(s)] pairs of [0.5 N/m, 30 kHz] forshorter cantilevers, and [0.01 N/m, 2 kHz] for the longer cantilevers(where ω_(s) is the fundamental resonant frequency in solution).

Smaller cantilevers with higher resonant frequencies are desirablebecause they allow faster imaging rates and permit the cantilever tip tomore closely track sample topography (see, e.g., Butt, Biophys. J. 60:777-785). Smaller cantilevers also are less affected by viscous damping,and are therefore more sensitive (see, e.g., U.S. Pat. No. 6,016,693).Smaller cantilevers have been described in Walters, et al., 1996, Rev.Sci. Instrum. 67: 3583-3590 (23 μm length); Walters, et al., 1997, SPIE,Proceedings Micro-Machining and Imaging 3009: 48 (26 μm length); andSchaeffer, et al., 1997, SPIE, Proceedings Micro-Machining and Imaging3009: 48 (9 μm length).

A number of groups have made efforts to generate high performancecantilevers. Stowe, et al., 1997, Appl. Phys. Lett. 7(1): 288-290,describe ultrathin (60 nm) silicon cantilevers with force constants onthe order of 10⁻⁶ and resonant frequencies in vacuum of 1.7 kHz. Whilethe performance of these cantilevers in solution was not examined, thedimensions of the cantilevers are such that they have a predictedresonant frequency in water of about 200 Hz. This frequency is too lowto be useful in most biological applications. Ried, et al., 1997, J.Microelectromechanical Sys. 6: 294-302, describe piezo resistivecantilevers with resonant frequencies of 6 MHz and spring constants of 2N/m. However, these types of cantilevers have relatively poor detectionsensitivity and are difficult to work with in solution, preventing themfrom being used productively in biological research. Such cantileversare used instead in data storage applications (see, e.g., Mamin andRugar, 1996, Appl. Phys. 79: 5644-5644) or in force-based magneticresonant imaging (Rugar et al., 1994, Science 264: 1560-1563).

High performance cantilevers specifically for use in biological researchhave been described (Walters et al., 1996, Rev Sci Instrum 67:3583-3590;Viani, et al., 1999, Rev. Sci. Instrum. 70: 4300-4303). The bestcantilevers thus far developed have resonant frequencies of 100-200 kHzin solution and spring constants of 0.1-0.2 N/m. However, improvementsin these cantilevers are largely limited by the lithographic and thinfilm deposition methods used for their fabrication.

U.S. Pat. No. 6,016,693 discloses a method for making a smallercantilever (e.g., 2-10 μm in length). The method comprises fabricating a“sacrificial cantilever” of SiO₂ and depositing a layer of materialwhich will form the final cantilever onto the sacrificial cantilever.The sacrificial cantilever is then etched away.

U.S. Pat. No. 5,666,190 discloses a compound cantilever for a scanningprobe microscope which includes a bending portion and a vibratingportion. The vibrating portion has a lower mechanical resonant frequencythan the bending portion. The cantilever is fabricated from two fusedsilicon oxide wafers.

SUMMARY OF THE INVENTION

The invention provides high performance cantilevers for Atomic ForceMicroscopes (AFMs), as well as methods for making and using the same. Inone aspect, the invention provides a cantilever with resonantfrequencies in the range of 1-100 MHz in solution for cantilevers with aspring constant of 0.1 N/m. At the high end, this resonant frequency isapproximately one to three orders of magnitude better than the bestcantilevers that are currently available.

In one aspect, the invention provides a cantilever for use in a scanningprobe microscope comprising a width to thickness ratio of about 3:1 orless and which is smaller in at least one dimension than about 5 μm.More preferably, the cantilever comprises a width to thickness ratio ofabout 1:1 or less.

In another aspect, the invention provides a cantilever for use in ascanning probe microscope whose resonance frequency is reduced by lessthan 70% in solution compared to its resonance frequency in air.

In a further aspect, the invention provides a cantilever for use in ascanning probe microscope, wherein the body of the cantilever comprisesa carbon nanotube.

Preferably, the cantilevers have a resonant frequency equal to or above10 kHz. More preferably, the cantilevers have a resonant frequency equalto or above 100 kHz.

Cantilevers may be fabricated from a variety of materials, including,but not limited to silicon, silicon nitride, silicon dioxide, a metal(e.g., gold, aluminum, silver, or nickel), a plastic, and asilicon-based rubber (e.g., PDMS). The metal gold, aluminum, silver andnickel.

In one aspect, the cantilever comprises a reflective portion. In anotheraspect, the cantilever comprises a conductive material.

The invention also provides a method for producing a cantilevercomprising providing a starting material; exposing the starting materialto an ion beam; and removing molecules from the starting material togenerate a cantilever which has a width to thickness ratio of about 3:1or less and which is smaller in at least one dimension than about 5 μm.

The invention further provides a method for producing a high performancecantilever comprising: providing a starting material; exposing thestarting material to an electron beam; and depositing molecules on thestarting material to generate a cantilever which has a width tothickness ratio of about 3:1 or less and which is smaller in at leastone dimension than about 5 μm.

In one aspect, the methods further comprise the step of imaging thestarting material at one or more time intervals. The starting materialmay comprise silicon, silicon nitride, silicon dioxide, or a metal. Themethod can be used to generate cantilevers comprising a resonantfrequency above at least about 10 kHz, and preferably, above at leastabout 100 kHz. The cantilever may comprise a spring constant of about1-10⁻⁶ N/m.

Starting materials may comprise materials of a variety of shapes. Forexample, the starting material may be a beam, a film, a sheet, aV-shaped material, or a rectangular shaped material. In one aspect, thestarting material is itself a cantilever.

In one aspect, a tip is generated at the end of the cantilever. Forexample, a tip may be fabricated using electron beam deposition.

In one aspect, the cantilevers produced by the methods described abovecomprise a conductive material.

The invention also provides a method of measuring the property of acantilever comprising measuring the deflection of any of the cantileversdescribed above.

The invention further provides a method for measuring a property of asample, comprising: detecting an interaction between a cantileveraccording to the invention and a sample, wherein the interactionprovides a measure of the property of the sample. The property maycomprise one or more surface features of the sample. In one aspect, thecantilever further comprises one or more biological molecules and theone or more biological molecules interact with one or more molecules ofthe sample. In another aspect, the biological molecule binds to the oneor more molecules. In a further aspect, the one or more biologicalmolecules is selected from the group consisting of: nucleic acids,proteins, polypeptides, peptides, receptors, ligands, enzymes, antigens,drug molecules, therapeutic agents, lipids, lipid bilayers, detergents,a cell membrane fraction, organelles, and zwitterions. The sample maycomprise one or more of: a cell, nucleic acids, proteins, polypeptides,peptides, receptors, ligands, enzymes, antigens, drug molecules,therapeutic agents, lipids, a cell membrane fraction, organelles, andmicroorganisms.

The invention additionally provides a method for fabricating ananostructure comprising: providing a substrate comprising a pluralityof molecules; and using a cantilever as described above to move one ormore molecules on the substrate to a desired position on the substrate.In one aspect, the cantilever is used to create a data structure on thesubstrate.

BRIEF DESCRIPTION OF THE FIGURES

The objects and features of the invention can be better understood withreference to the following detailed description and accompanyingdrawings. The drawings are not to scale.

FIGS. 1A-C show scanning electron micrographs of compound cantilevers,produced by electron beam deposition according to one aspect of theinvention. FIG. 1A shows a 12 μm long cantilever grown off the end of astarting material which is a microfabricated silicon nitride cantilever.FIG. 1B shows a 1.5 μm long cantilever grown near the apex of the tip ofa silicon starting material which can be interrogated through motions ofthe starting material. FIG. 1C shows a cantilever grown offend ofsilicon nitride starting material with a pad constructed in the middleThe pad was constructed by depositing 4-5 electron beam “spikes”parallel to the plane of the silicon nitride starting material.

FIGS. 2A-2I show a method of making a cantilever using an FIB processand the properties of cantilevers produced by the method. FIGS. 2A-Cillustrate steps in an FIB process to produce an optimal highperformance cantilever according to one aspect of the invention. FIGS.2D and E are scanning electron micrographs (SEMs) of ion beam modifiedcantilevers. FIG. 2D shows an SEM of cantilever 1 from, Example 1, Table2. The two legs of the cantilever are 0.75 μm wide and 21 μm in length.The reflective pad is 15.0 μm long and 20.0 μm wide. FIG. 2E is ascanning electron micrograph of cantilever 3 from, Example 1, Table 2.The legs of cantilever 3 are approximately 20 μm in length and 1.2 μm inwidth. The dashed line shows the size of the original pad. FIGS. 2F andG show a power spectrum of cantilever 1 in air and water. Thefundamental resonant frequency is 127 kHz in air and 51 kHz in water. Inboth cases, there is a low frequency peak centered at f=0 associatedwith 1/f and other electronic noise. FIGS. 2H-I show the thermal noiseof cantilevers in water from 100 Hz-10 kHz. FIG. 2H shows a conventionalE Microlever cantilever, while FIG. 2I shows the thermal noise ofcantilever 1.

DETAILED DESCRIPTION

The invention provides high performance-cantilevers with optimalcombinations of high resonant frequencies and low force constants. Inone aspect, AFM cantilevers with spring constants in the range 1-0.01N/m, and preferably in the range of 0.1-10⁻⁶ N/m, with (fundamental)resonant frequencies in aqueous solutions of 1-100 MHz are provided. Inone aspect, a high performance cantilever according to the invention isgenerated by modifying a starting material by focused ion beam millingto remove molecules from the starting material to generate a geometrywhich minimizes damping of resonant frequency in solution. As analternate, or additional approach, electron beam deposition methods areused to add molecules to starting materials to provide this geometry.

Preferably, the cantilevers have a width to thickness ratio which isless than about 3:1 and more preferably, is about 1:1. More preferably,the cantilevers have at least one dimension which is smaller than about5 μm. The high performance cantilevers according to the invention allowfaster scanning, increase the temporal resolution of force measurement,improve measurement sensitivity by reducing cantilever noise, andimprove sensitivity by reducing the cantilever spring constant.

Definitions

The following definitions are provided for specific terms which are usedin the following written description.

As used herein, a “cantilever leg” refers to a portion of a cantileverextending from its base or supported end.

As used herein, a “cantilever tip” refers to the portion of thecantilever for interacting with a sample.

As used herein “a biological molecule” refers to a molecular derivedfrom a cell or organism, which may be produced by a cell or organism orwhich is a synthetic or mutated or modified copy of such a molecule.

As used herein, “a biological molecule which interacts with one or moremolecules” of a sample refers to a biological molecule whose contactwith one or more molecules in a sample causes a measurable change in theproperty of a sample, as determined in an assay suitable for measuringthe property.

As used herein, “proximity” refers to within about 100 nm of a sample.

High Performance Cantilevers

With all other things being equal, the higher the resonant frequency ofan AFM cantilever the better its performance. A high resonant frequencyhas several benefits. For example, in contact mode imaging, a highfrequency allows a cantilever tip to more closely track sampletopography (see, e.g., Butt, et al., 1993, J. Microsc. 169: 75-84). InAC imaging modes, imaging speed is limited by a combination of theresonance quality factor (Q) and the resonant frequency. Thus, for anygiven Q, the higher the resonant frequency, the faster the feedback,which in turn allows for faster imaging. There are correspondingbenefits in force measurements. Higher resonant frequencies allow forbetter temporal resolution (see, e.g., Butt and Jaschke, 1995,Nanotechnology 6: 1-7). In general, cantilevers with higher resonantfrequencies produce measurements less affected by background in a givenbandwidth because thermal noise is spread over a greater frequency range(Walters, et al., 1996, Rev. Sci. Instrum. 67: 3583-3590; Viani, et al.,1999, Rev. Sci. Instrum. 70: 4300-4303).

For cantilevers used to evaluate biological samples, it is alsoparticularly desirable to use lower spring constants so that less forceis imparted on the sample, e.g., to minimize sample destruction.

Basic Cantilever Design

There are two common cantilever geometries, diving boards or rectangularcantilevers, and V-shaped cantilevers. The diving board is a simpleend-supported beam and thus the spring constant is given by

$\begin{matrix}{k_{Beam} = \frac{{Ewt}^{3}}{4l^{3}}} & (1)\end{matrix}$

where w is the width of the cantilever, t is the thickness of thecantilever, l is the length of the cantilever and E is the elasticmodulus of the cantilever material.

V-shaped cantilevers can be modeled using a double beam approximation,although for short cantilevers, where the width becomes significantrelative to the length, this approximation fails (Sader, 1995, Rev. Sci.Instrum. 60: 4583-87). However, the resonant frequency for a simpleV-shaped beam in vacuum (and to a good approximation in air) is givenby:

$\begin{matrix}{\omega_{Beam} = {\frac{t}{2\pi\; l^{2}}\sqrt{\frac{E}{\rho_{C}}}}} & (2)\end{matrix}$where p_(C) is the cantilever material density or, for a composite beam,p_(C), is the average density of the beam.

There is a significant reduction of the resonant frequency of acantilever when it is placed in solution (Sader, 1998, J. Appl. Phys.84:64-76; Butt et al., 1993, supra, Schaeffer, et al., 1996, supra). Asimple relationship for a beam having either a diving board or V-shapedconfiguration that gives reasonably good agreement with experimentalvalues (at the fundamental frequency) is

$\begin{matrix}{{\frac{\omega_{s}}{\omega_{v}} = \left\lbrack {1 + \frac{\pi\;\rho_{F}w}{4\rho_{C}t}} \right\rbrack^{{- 1}/2}},} & (3)\end{matrix}$where p_(F) is the density of the fluid in which the cantilever isimmersed, and ω_(s) and ω_(v), refer to resonant frequencies in solutionand vacuum respectively (Chu, W.-H., 1963, Tech. Rep. No. 2, DTMB,Contract Nos.-86396(X), Southwest Research Institute, San Antonio,Tex.). For most presently used cantilever geometries, this ratio isapproximately 0.25, resulting in a four-fold drop in the resonantfrequency when they are used in solution.

Equations (1)-(3) can be used to derive the design parameters ofoptimally performing cantilevers. For example, to achieve highfrequency, cantilevers need to be short or thick, while low springconstant cantilevers should be long or thin. To improve both resonantfrequency and provide a lower spring constant, cantilevers must be shortand thin. For a cantilever that operates in air, a 10-fold reduction inlength and a 10-fold reduction in thickness keeps the spring constantthe same while increasing the resonant frequency by a factor of 10. Onthe other hand, a 10-fold reduction in thickness and a 3-fold reductionin length keeps the resonant frequency close to constant while reducingthe spring constant by approximately 30-fold. Thus, the exact desireddimensions of a cantilever will depend on whether spring constant orresonant frequency is being optimized.

An important feature of cantilever design identified herein is tooptimize cantilever geometry. From equation 3, it can be shown that foran appropriate combination of cantilever width and thickness, thereduction of resonant frequency in solution can be virtually eliminated.For example, for a silicon nitride cantilever with a width to thicknessratio of 1, ω_(s) is 0.9 times that in vacuum. Thus, while cantileverwidth has no effect on ω_(v), decreasing the width effectively increasesω_(s). In addition to the change in ω_(s), the spring constant decreaseslinearly with the width. The cantilevers of the present invention takeadvantage of these property changes that occur when cantilever geometryis optimized, i.e., such as when cantilever widths are minimized.

Therefore, in one aspect, a cantilever geometry is selected whichreduces the damping of the cantilever's resonant frequency in solution.Preferably, the resonant frequency of the cantilever is reduced by lessthan 75% of the resonant frequency in air. More preferably, the resonantfrequency is reduced by less than about 70%, less than about 65%, lessthan about 60%, less than about 55%, less than about 50%, less thanabout 45%, less than about 40%, less than about 35%, less than about30%, less than about 25%, less than about 20%, or by less than about 15%of the resonant frequency in air.

One way in which this reduction in damping is achieved is by producing acantilever whose body has a cross-section of about 10:1 or less, about5:1 or less. More preferably, the ratio is about 3:1 or less. Still morepreferably, the width to thickness ratio is about 2:1, about 1.5:1, andmost preferably, about 1:1 or less. In one aspect, the size of thecantilever in at least one dimension is less than about 5 μm (e.g.,about 4.0 μm, about 3.0 μm, about 2.0 μm, about 1.0 μm, about 0.5 μm,about 0.2 μm, about 0.1 μm, about 0.05 μm or less).

Materials for fabricating cantilevers can vary. However, in one aspect,a cantilever should be least partially reflective so as to enable itsuse in a laser-based detection scheme such as optical beam deflection(OBD) or interferometry. Generally, silicon is a material with suitablereflectivity when the thickness of the cantilever is chosen to equalabout a quarter of the wavelength produced by laser being used fordetection. For example, the reflectivity of a 50 nm thick siliconmembrane illuminated with 670 nm laser light and immersed in water isapproximately R=0.6. However, a metal, such as gold, silver, aluminum,or nickel, also may be used to generate a cantilever with suitableproperties (see, e.g., U.S. Pat. No. 6,016,693). Additional materialssuch as SiO₂ or Si₃N₄ may be used.

In another aspect, a cantilever material is selected which isconductive. For example, the cantilever, is silicon, a carbon nanotube,or a metal.

Other materials for cantilevers can be selected which maximize theflexibility and/or width to thickness ratios and/or performanceproperties (e.g., maximize resonance frequencies, minimize springconstants, minimize noise and the like).

In one particularly preferred embodiment, the body of the cantilevercomprises a carbon nanotube. Carbon nanotubes are macro-molecules ofcarbon, analogous to a sheet of graphite, however, rolled into acylinder. In such a coiled geometry, the carbon arrangement becomes verystrong. Being one giant molecule, carbon nanotubes have unusualmechanical and electrical properties. The conductivity of single wallcarbon nanotubes can vary from semi-conductive to metallic depending onthe chiral angle of the tube and its diameter.

Methods for Making Cantilevers

The design parameters described herein enable the fabrication of highperformance cantilevers. It should be obvious to those of skill in theart that the exact method for producing a cantilever with the parametersdescribed above (e.g., width to thickness ratio which minimizes damping,such as a ratio of about 3:1 or less) may vary and that new methods offabrication may evolve to achieve such parameters. All such methods areencompassed within the scope of the invention.

In one aspect, a suitable starting material is selected and moleculesare added to or removed from the material to produce a structure havingthe dimensions described above. Preferably, the starting material issilicon, silicon dioxide, silicon oxide, silicon nitride, or a metal(e.g., gold, silver, aluminum, nickel) which comprises a base or end forsupporting or mounting during the fabrication process. The startingmaterial also can be a silicon-based rubber such as polydimethylsiloxaneor PDMS, or even plastic.

The starting material can be a variety of shapes, e.g., a film, a sheet,a beam, a brick, a cube, a polygon, a v-shaped material, rectangularshaped material, an irregularly shaped material, and the like. Thestarting material can even be a conventional cantilever. In one aspect,molecules are removed from the starting material by exposing thestarting material to an ion beam. In another aspect, molecules are addedto the starting material by exposing the starting material to anelectron beam. Lithographic techniques may also be used.

In part, methods of fabricating cantilevers will depend on the nature ofthe starting material. For example, cantilevers comprising carbonnanotubes can be fabricated using chemical vapor deposition process togrow nanotubes of controlled length and diameter. Depending on thegrowth process, the length of the tubes can be from approximately 100nanometers to several microns. Diameters can vary from 1 to 20nanometers. In one preferred aspect, the body of a carbon nanotubecantilever is about 1-10 nm in diameter, more preferably, from about 1to 5 nm in diameter, and still more preferably, about 2 nm in diameter.

The carbon arc method (Ebbesen and Ajayan, 1992, Nature 358: 220-222)can be used to generate a carbon nanotube. This method creates nanotubesthrough the arc-vaporization of two carbon rods placed end to end whichare separated by about 1 mm. A direct current of 50 to 100 A driven byapproximately 20 V creates a high temperature discharge between the twoelectrodes. The discharge vaporizes one of the carbon rods and forms asmall rod shaped deposit on the other rod. Producing nanotubes in highyield depends on the uniformity of the plasma arc and the temperature ofthe deposit form on the carbon electrode.

The laser vaporization method produces single-wall carbon nanotubes inhigh yields. In this method, a graphite target is heated to 1200° C. ina quartz tube. A Nd-YAG laser ablates carbon off of the graphite target.Soot from the ablation process contains a high percentage of single wallcarbon nanotubes.

AFM techniques additionally, or alternatively, can be used to produceand/or refine the geometry of a carbon nanotube.

Focused Ion Beam Milling

As noted above, fabrication of AFM cantilevers is presently largelylimited by the optical methods available for the lithography and thetechnical difficulties of producing beams with widths or lengths smaller2 μm. To overcome these limitations, in one exemplary aspect, theinvention uses ion beam and electron beam methods to produce cantileversthat have dimensions of 10's of nanometers in at least one axis.

Focused ion beam (FIB) milling is a technology which has been widelyused in the semiconductor and materials science fields. It isessentially the reverse of sputtering, where an ionized gas (oftenargon) is accelerated with relatively low energies (100's to 1000's ofeV) against a surface. These ions dislodge material at the surface,thereby etching it. In simple terms, it might be thought of as an atomicsandblaster. By using focused ion beams, etching can be extremely local.

FIB is routinely used to modify surfaces on a length scale of <16nanometers (Johnson, 1984, In Ion Bombardment Modification Of Surfaces,Auciello and Kelly (eds) Elsevier Publishers B. V) and is probably mostwidely used for “editing” semiconductors. However, it also is commonlyused by material scientists to “cut” thin sections (50 nm) of extremelyhard materials for transmission electron microscopy. FIB has been usedin atomic force microscopy to modify AFM tips to produce very highaspect ratio tips for imaging trenches and other deep structures, buthas not be used to produce the body of a cantilever.

In one aspect, the invention provides a method for constructing acantilever with a high resonant frequency which comprises using ascanned beam etching technique, such as FIB milling, to produce the bodyof the cantilever. Initially, a desired spring constant is selected. Forexample, cantilevers with spring constants in the range 0.01-0.5 N/mhave been successfully used in a wide range of biological experiments.Therefore, preferably, a cantilever is designed which provides a forceconstant of approximately 0.01 N/m. More preferably, the cantilever alsohas a resonant frequency of at least about 0.1-100 MHz.

The method comprises providing a starting material and exposing thestarting material to an ion beam from an ion source. A suitable ionsource can comprise a liquid metal ion source (e.g., a Gallium or Indiumsource). Preferably, the source comprises a relatively high intensity(e.g., approximately 10⁶ A/cm²sr) and a small emission area(approximately 10 nm). A small emission area permits strong focusing ofthe ion beam by an optical system integrated with the ion source.

Preferably, the ion beam source comprises a column in which ions aregenerated, accelerated and focused (e.g., by electrostatic lenses). Inone aspect, the ion beam source communicates with a high vacuum chambercomprising a stage on which the first cantilever can be mounted.Suitable ion beam workstations include the FEI 610 focused ion beamworkstation or FEI 200 focused ion beam instrument (FEI, Hillsboro,Oreg.).

Preferably, the beam energy from the ion source is from about 10 toabout 50 kV, and the spot size is less than about 100 nm. Morepreferably, spot size is less than about 10 nm. The ion beam current mayrange from about 1 to about 150 pA. Ion densities are within the rangeof about 1-20 A/cm².

Sputter erosion of the starting material by the ion source enables localremoval of material from the starting material. A single beam can beoperated in an imaging mode by using a low beam intensity. In theimaging mode, material to be removed is identified. In one aspect,imaging of the cantilever is performed by monitoring secondary electronsgenerated during the sputtering process. Their production can bemonitored means of a secondary electron detector and used to produce animage. Thus, high-resolution ion-beam induced secondary electron imagescan be generated which can be used to monitor the fabrication process.

The intensity is then increased and ion beam is used to etch away theappropriate material. The structure is then imaged again to verify thesuitability of the new structure. Generally, a cantilever can be milledin about 10 to 100 minutes using the method according to the invention.However, etch rates may vary depending on the material chosen for thecantilever. For example, for silicon nitride, typical etch rates are onthe order of 5 μm³/s.

As with conventional ion beam milling, the process of removing moleculesfrom the starting material can be implemented using a processor incommunication with the ion beam and with an image detector which detectssecondary electrons or other imaging data generated by the startingmaterial being milled. Preferably, the processor is also incommunication with a work station with which a user can interface. Inone aspect, by placing a stylus on a display of the work station (e.g.,a monitor of a standard computer) which displays an image of thestarting material, the user draws a particular shape or geometry to bemilled and the processor uses this information to control the millingprocess (e.g., by controlling beam energy, beam direction, and thelike).

Generally, the beam can be focused anywhere along the length of thestarting material. In one aspect, the starting material is held ormounted at one end (e.g., its base) to a support (e.g., such as a glassslide) and the ion beam is focused anywhere along the length of thematerial distal from the base to mill at least a portion of the startingmaterial to a geometry which minimizes damping in solution of thecantilever's resonant frequencies as described above (e.g., providing awidth to thickness ratio of about 3:1, and preferably, about 1:1).Preferably, the ion beam mills a structure of a desired geometry at adistance from the base which permits light at an angle from about 1° to180°, preferably, from about 10°-100°, and more preferably, from about20-90°), to be reflected from the surface of the desired structure.

In one aspect, the cantilever has one or more legs. Legs can be of avariety of dimensions. For example, the legs of the second cantilevermay be about 100 nm thick, 100 nm wide and 3 μm long. Preferably, thespring constant of the second cantilever is about 0.1 N/m while theresonant frequency of the cantilever in solution is about 10 MHz. FIGS.2A-C show a schematic of one exemplary cantilever design, and themilling steps performed to construct it.

As shown in FIGS. 2A-C, a conventional diving board AFM silicon nitridecantilever from ThermoMicroscopes can be used as a starting material.This cantilever is 200 μm long, 20 μm wide, and 600 nm thick, and has asputtered gold reflective surface. It is also tip-less (however, themethod shown applies equally well to cantilevers comprising tips).However, in general, the approach shown in the Figure may be used withany type of starting material which need not be a cantilever.

In the aspect shown in FIG. 2A, the starting material is cutapproximately in half, removing material (shaded in the Figure) in orderto make the starting material stiffer (preferably, to about 10 N/m). Asshown in FIG. 2B, the front portion of the starting material is thenmilled to produce an approximately 2 μm×2 μm rectangle attached to thestarting material by two legs that are about 100 nm in diameter, againremoving material indicated by shading in the Figure. As shown in FIG.2C, the milled starting material is then turned on its side and the legsare first thinned on top, removing the reflective gold coating which isvery dense and hence contributes disproportionately to the secondcantilever's effective mass. The legs are then thinned on the bottomside to a thickness of about 100 nm. Preferably, the underside of thereflective pad is also be thinned by about a few hundred nanometers, toreduce the effective mass and improve the resonant properties of thenewly formed cantilever.

Although in the Figures, a conventional cantilever is used as thestarting material, as discussed above, many other starting materials canbe used (e.g., thin films, sheets, bricks, beams, and the like ofsilicon, silicon nitride, silicon dioxide, metals, plastic, etc.).

In another aspect, a cantilever with legs of about 40 nm in width, about40 nm thick and about 900 nm length is produced, thereby generating acantilever with a spring constant of 0.1 N/m and resonant frequency insolution of about 60 MHz.

Preferably, cantilevers according to the invention have resonantfrequencies in the range of about 0.1-100 MHz in solution. Morepreferably, resonant frequencies are above 10 MHz. In one aspect, thespring constants of the cantilevers range from about 1-10⁻⁶ N/m with(fundamental) resonant frequencies in aqueous solutions of 0.1-100 MHz.Cantilevers having legs with a thickness of about 100 nm or less andwidths of about 100 nm can be produced. It should be obvious to those ofskill in the art that the exact dimensions of the cantilever can bevaried by a user to achieve selected criteria, such as desired resonantfrequencies and spring constants.

Low spring constant cantilevers are extremely appealing for theirpotential application to biological systems. As noted earlier, low forceconstants are likely to be less destructive for imaging of biologicalsamples and more sensitive in force measurements. In terms offabricating these cantilevers by focused ion beam milling, the approachis to achieve the spring constant desired while maintaining as high aresonant frequency as possible. In one aspect, this is achieved byincreasing the length of the legs while keeping the leg width andthickness as small as possible. For example, a beam 25 μm long, withlegs that 100 nm thick and 100 nm wide, would have a spring constant of2×10⁻⁴ N/m and a resonant frequency in solution of about 150 kHz. For100 μm long legs, this becomes 3×10⁻⁶ N/m and 10 kHz. For thefabrication of these long legs, a V-shaped starting material (e.g., suchas a V-shaped cantilever) may be used as the starting material.

In some cases, it may not be necessary to truncate the startingmaterial. For example, a thicker starting material can be selected(e.g., about 2 μm) and can be used to provide a starting material thatis sufficiently stiff even at full length (e.g., by custom fabricationof a wafer of silicon nitride). Alternatively, where a lower resonantfrequency is acceptable, a softer starting material may be selected(e.g., such as plastic or a silicon-based rubber such as PDMS).

In a preferred aspect, the cantilever formed from the starting materialhas a small reflective pad at a portion of the starting material distalfrom the base (e.g., such as at the end of the starting material) toenable imaging of cantilever deflections. The pad end loads the leg,while the mass of the leg is distributed along its length. Thus, the padacts as a large end-loaded mass that significantly reduces the resonantfrequency of the cantilever. For a uniform straight beam, the effectiveend-loaded mass is 0.25 times the total mass. The resonant frequencyscales with m^(−1/2), where m is the end-loaded mass, so the pad reducesthe resonant frequency by a factor of ˜10. The reflective pad alsodominates the hydrodynamic properties of the cantilever in solution,further degrading performance. For example, the mass of the pad may beapproximately 100 times that of the effective mass of the legs.

From a design standpoint, the size of the reflective pad must be largeenough to reflect sufficient light from a conventional optical lever,however, small enough to preserve desired performance properties of thecantilever. Based on dimensions of conventional cantilevers, a pad ofabout 10 μm×10 μm is adequate.

Treating the pad as a mass end loading one of the legs as describedabove, the expected resonant frequency drop is from about 10 MHz toabout 2 MHz. In use, an additional reduction of the frequency ofapproximately 2-fold to about 1 MHz will occur due to damping insolution. However, this is still a dramatic improvement over presentlyavailable cantilevers with similar spring constants that have resonantfrequencies in solution of order 10 kHz. 1 MHz is also well within thedetection bandwidth of many commercial AFMs, such as the Nanoscope IIIfrom Digital instruments. The smallest pad that will produce sufficientreflection is on the order 2 μm×2 μm.

Electron Beam Deposition for Generating Cantilevers

In another aspect, the invention provides a method for fabricating ahigh performance cantilever by electron beam deposition. It has longbeen known to electron microscopists that focusing an electron beam atone position will produce “contamination.” This contamination resultsfrom the ionization and polymerization of surface diffusing pump oil.This was apparently first exploited in scanned probe microscopy toproduce tips for scanning tunneling microscopy (Akama et al., 1990, J.Vac. Sci. Technol. A8: 429-433). Subsequently Keller and Chou, 1992,Surf. Sci., 268: 333-339, and Ximan and Russell, 1992, Ultramicrosc. 42:1526-1532, demonstrated that very sharp and high aspect ratio AFM tipscould be produced by depositing an “e-beam” tip on the pyramidal tip ofa conventional AFM cantilever. These are now widely used in biologicalresearch.

In contrast to the prior art, the present invention uses e-beam methodsto produce the body of an AFM cantilever by growing e-beam material(e.g., such as hydrocarbons or silicon) on a starting material (e.g.,such as those described above). Generally, molecules from the e-beam canbe deposited anywhere along the starting material (e.g., parallel to aplane of the starting material, at an end of the starting material,etc.). As with ion beam milling, the fabrication process is monitored atdifferent time intervals until a suitable geometry and/or dimensions areachieved and can be controlled using a processor in communication withan electron beam source and a work station.

In one aspect, a starting material is mounted on a support or mount(e.g., such as a glass substrate) and e-beams are used to grow acantilever at the end of a starting material which is pointed toward theelectron beam source of a standard scanning electron microscope (SEM).The beam may be adjusted to accommodate mechanical drift in themicroscope used and can be refocused periodically to maintain a smallspot at the growing end of the cantilever. The cantilever grown may havea varying diameter so as to form a slight taper, however, in onepreferred embodiment, tapering is minimized by more frequent refocusingof the electron beam and/or by minimizing surface diffusion of activatedmolecules out of the irradiation volume. E-beam structures can beproduced using high performance field emission SEMs as are known in theart.

The resonant frequency of cantilevers so formed is very high and can beestimated using the formula: ω=(klm*)^(1/2), where m* is the effectivemass. This is another form of equation (2), that does not requireexplicit values for the material modulus.

Suitable materials for cantilevers include those with elastic moduli onthe order of 100 Gpa, such as crosslinked polymers, silicon, or siliconnitride (see, e.g., FIGS. 1A-C). Pads may be constructed on the startingmaterial by depositing electron “spikes” parallel to the plane of thestarting material and in close proximity to each other (See, e.g., FIG.1C).

Tips of cantilevers generated by ion beam milling or by electrondeposition can be fabricated by means known in the art. In one aspect ofthe invention, electron beam deposition is used to fabricate a tip atthe end of a cantilever formed by ion beam milling. Tips may also beadhered to the end of a cantilever distal from the base, although thisis less optimal as the size of the cantilever decreases.

In fabricating cantilevers, the design of the tip may be optimized tooptimize the coating characteristics of the tip. For example, it may bepreferable to make the tip more blunt than in a standard cantilever. Thesurface of the tip may additionally be chemically modified usingdifferent silanes or surface modifiers as are known in the art.Alternatively, where a conventional cantilever is used as the startingmaterial to generate a high performance cantilever, the tip of the firstcantilever in the compound cantilever may be left intact during thefabrication process.

Physical properties of the high performance cantilevers generated can beevaluated can include but are not limited to, one or more of: resonantfrequencies, spring constants, Q value, and noise characteristics.

Resonant frequencies can be measured directly from power spectra ofcantilever noise measurements as is known in the art. Spring constantscan be determined from thermal noise data, by fitting the resonant peak(Hutter and Bechoder, Rev. Sci. Instrum 64: 1868-1873. 1993) or bysimply evaluating the RMS amplitude. Butt and Jaschke, Nanotechnology 6:1-7, 1995, also describe methods for determining thermal noise. Saderalso describes methods for determining resonance frequencies and/orspring constants (see, e.g., Sader, Rev. Sci. Insrum. 60: 4583-87: 1995.

Q values also may be measured using means known in the art (see, e.g.,Stowe et al., 1997, supra). This is particularly preferred for AFMapplication such as tapping mode imaging in air/vacuum environmentswhere feedback times are in part limited by cantilever Q's.

AFM Microscopes for Small Cantilevers

The generation of very small cantilevers offer a number of advantages asdescribed above. Preferably the cantilevers are used in a microscopewith a large bandwidth. Schaeffer and Hansma, 1999, J. Appl. Phys. 84:4661-4666, and Viani, et al., 1999, supra, report an AFM speciallydesigned for working with small cantilevers. This microscope isdifferent from conventional AFMs in that it allows the detection laserto be focused to a nearly diffraction limited spot onto a cantilever,enabling sufficient reflection from the cantilever. This microscope isbased on an optical lever detection system with a diode laser forreflecting light off a cantilever which is detected by a split segmentphotodiode. In a particularly preferred embodiment, the microscope ismodified to comprise a high speed electric circuit which couples thephotodiode to a imaging system.

Cantilever movement preferably is monitored by the high speed positionsensor (e.g., segmented photodiode) described above. Signals from thesensor can be used to determine probe oscillation amplitude, frequency,and phase, as well as other parameters, and to measure the probe-sampleinteractions based on determined probe parameters. A data acquisitionsystem can use this measurement as a feedback signal to control therelative position of the cantilever and sample so as to keep thecantilever-sample interaction constant during data acquisition. In oneaspect, a display device is coupled to a processor receiving informationfrom the data acquisition device which can displays graphicrepresentation of measurements obtained (e.g., a histogram) results in avisual image, such as a histogram.

For data collection, a data acquisition device for writing data to acomputer memory is preferably in communication with the detection systemof whatever AFM microscope is used, e.g., receiving signals from thesegmented photodiode, for example, or from a tunneling electrode. In oneaspect, the data acquisition device comprises a PCI board which is usedin a standard PC-type computer. In one preferred aspect, the boardcomprises a variable sampling rate of up to about 100 MHz or faster.Preferably, the board can acquire at least about 8 bit data at itshighest speeds, and more preferably, the board can acquire at leastabout 10, at least about 12, at least about 15, at least about 18, or atleast about 20 bit data. A number of suitable software packages may beused to control data acquisition, such as the LabVIEW software packagefrom National Instruments (at http://www.ni.com/support/) to controldata acquisition (see, e.g., Heinz et al., 2000, J. Phys. Chem. B. 104:622-626. 2000; Koralek, et al., AD ⁻01. Phys. Lets. 76: 2952-2954).

Methods for Using High Performance Cantilevers

Biological Applications

The cantilevers according to the invention are ideal for use in assayswhich require an evaluation of the surface properties or features ofsamples, such as biological samples. In one aspect, a cantilever is usedin a method for detecting a biochemical reaction, as described in U.S.Pat. No. 5,620,854. The method comprises measuring signals emittedduring the time sequence of the reaction using the stationary modeoperation of a scanning probe microscope, such as an AFM. The cantilevercan be used to process signals emitted directly from the sample orthrough a medium which contains the sample. By using the AFM device in astationary mode, the cantilever's tip can be used to measurecharacteristic motions (e.g., such as vibrations) or acoustic signals(e.g., such as frequencies) created or emitted by a sample (e.g., acell, biomolecule, and the like). In one aspect, an intermediarymolecule (e.g., an enzyme, colloidal particle, gold ball, etc.) is bebound to the sample and the motion of the intermediary molecule ismonitored (e.g., by laser interferometry) to monitor the motion of thesample.

The cantilever is used in a contact or non-contact mode to detect suchprocesses as a change in configuration of an enzyme, polymerization, eggfertilization, viral attack on a cell, conformational changes ofmolecules, appendage motion, replication (cell division), viral attack(membrane motion), the intermolecular transfer of phosphate theinteraction of proteins and ligands (e.g., such as drug molecules orother therapeutic agents), the unfolding and refolding of proteins, andother biochemical reactions occurring in, or on, a cell. Preferably,reactions are monitored over time. More preferably, monitoring isperformed in a thermally stabilized environment to eliminatetemperature-induced drift. However, the temperature or the chemicalenvironment may be changed to slow down rates of reaction to betteridentify a sequence of reactions.

In one preferred aspect of the invention, a cantilever designed as aboveis used to image the surface topography of a biological sample (see,e.g., as described in U.S. Pat. No. 5,874,668). Preferably thecantilever is used in conjunction with an optical system as describedabove.

In one aspect, the hp cantilever is coated with or coupled to anamphipathic molecule, such as a lipid molecule, detergent, zwitterion,and the like. The cantilever may be coated at the tip, along the body ofthe cantilever, or over a portion of the body of the cantilever and/ortip. Alternatively, or additionally, the cantilever can be coated with aphotoactivatable material, a conductive material, a semiconductivematerial, or a pharmaceutical coating (e.g., comprising a biologicalmolecule for interacting with the sample).

Suitable pharmaceutical coatings include, but are not limited to, anantibody, receptor ligand, enzyme, protein, polypeptide, peptide,antigen, or chemical, that is capable of interacting specifically with amolecule or site on a molecule of interest on a sample. When thecantilever comes into contact with a molecule or portion thereof on thesample which binds to a biological molecule coating the cantilever, astronger force is needed to separate the cantilever from the sample thanwhen no binding occurs. This force can be measured using AFM to provideinformation as to the nature of one or more molecule(s) in a sample.Methods of functionalizing cantilevers are known in the art and aredescribed in U.S. Pat. No. 5,874,668, for example.

Functionalized cantilevers can be used in a variety of diagnostic assaysto detect unique surface features (e.g., such as molecules expressed) ofa biological sample (e.g., a cell, microorganism, a bodily fluid, andthe like) which are correlated with disease or an abnormal physiologicalresponse. In one aspect, the cantilever comprises a molecule whichinteracts with a marker of a disease or an abnormal physiologicalresponse, and detecting changes between the interaction of thecantilever and the sample is used to identify the presence of the markerin the sample. In one preferred aspect, an array of cantilevers isprovided comprising a plurality of cantilevers, each comprising adifferent binding partner stably associated with the cantilever. Thisenables high throughput detection of different molecules in a sample.

The cantilevers according to the invention also can be used to screenfor molecules which alter the interactions between binding partners, forexample, to screen for drugs that modulate receptor:ligand interactions,by contacting the sample with a molecule (e.g., a drug, therapeuticagent or candidate agent) and identifying molecules which alterinteractions between the cantilever and the sample.

In another aspect, cantilevers are used in methods for detecting nucleicacid polymerization (e.g., such as DNA replication) (see, e.g., U.S.Pat. No. 6,280,939). Preferably, the cantilever is configured to reactto the movement of a polymerase during a polymerization reaction todetect the movement of a growing polynucleotide chain through thepolymerase during nucleotide incorporation. More preferably, thecantilever is part of an optical system which comprises a dataacquisition device capable of transforming incorporation data intonucleotide data (e.g., to obtain sequence information).

In a further aspect, an oligonucleotide or other nuclear acid probe isdeposited on a cantilever and the interaction between theoligonucleotide and a nucleic acid in a sample is monitored by detectingstress on the cantilever at a particular site (see, e.g., U.S. Pat. No.6,203,983) (e.g., at one or more locations on a substrate comprising aplurality of nucleic acids stably associated therewith).

In another aspect, cantilevers according to the invention are used tomap surface features of molecular libraries (e.g., a nucleic acidlibrary; protein, polypeptide, or peptide library, an antigen library, asmall molecule library, and the like) as described in U.S. Pat. No.6,287,765. The specific binding affinities of members of a molecularlibrary may be determined and correlated with the known address alibrary member on a substrate to identify library members with desiredcharacteristics (e.g., binding affinities). In one aspect, an array ofcantilevers is used to interrogate different members of the library.

In a preferred aspect of the invention, cantilevers are used to evaluatethe dynamics of lipid bilayer fusion. Important cellular processes suchas endo- and exocytosis, vesicular trafficking, synapse function,pinocytosis, and fertilization depend on the successful interactions,including fusion, between lipid bilayers. In one aspect, therefore, acantilever tip is coated with a lipid bilayer and brought into contactwith a lipid bilayer on a surface or substrate (which may be the sametype or a different type of lipid bilayer). The lipid bilayer on thesurface may be provided in the form of a cell, a cell membrane fraction,an organelle fraction, or a reconstituted cell membrane fraction. Thetwo bilayers are pressed together to compel fusion, and the associatedforces are measured. The dynamics at the cantilever can then be used toevaluate the dynamics of membrane fusion.

By using an AFM system as described above, different steps of the fusionprocess can be dissected and the time course of these steps monitored.In one preferred aspect, the dynamics of membrane fusion of a membranefraction from a diseased cell is examined to correlate changes inmembrane dynamics with abnormal physiological responses. In anotheraspect, a bilayer (e.g., from a cell, cell membrane fraction, and thelike) sample is contacted with an agent to evaluate the effect of theagent on the dynamics of membrane fusion. In a further aspect, theeffect of the agent is correlated with changes in membrane dynamicsassociated with an abnormal physiological response, i.e., to determinethe ability of the agent to restore the normal properties of themembrane.

Non-Biological Applications

Cantilevers also can be used in a variety of non-biologicalapplications. For example, the cantilevers can be used to measuremechanical properties of a sample (e.g., by nano-indentation, scratchtests, force modulation, and the like). Atomic force microscopy also canbe used to fabricate nanostructures (e.g., on silicon wafers, thin filmmagnetic read/write heads, and the like) (see, e.g., U.S. Pat. No.6,337,479) or to evaluate the properties of these nanostructures.

In one aspect, a cantilever according to the invention is used to obtain“vertical metrology” measurements, e.g., to determine tolerances of datastorage devices and semiconductor devices. For example, the cantileverscan be used to measure the of the recession of the pole tips of arecording head of a hard disk drive. The pole tips are the portions ofthe sensing or read/write element of the recording head which interfacemagnetically with the recording medium. During operation, it isdesirable to minimize the spacing between the pole tips and the magneticlayer of the hard disk, thereby maximizing the signal-to-noise ratioobtained from the read element and the density of the data that can bewritten to the disk. Vertical metrology data can be obtained as isdescribed in U.S. Pat. No. 5,898,106, for example.

Cantilevers also can be used to create surface features on a substrate.For example, cantilevers can be used to create ultra high densitystorage media. AFM comprising a cantilever according to the inventioncan be used to move atoms or molecules around on an electricallyconductive surface (i.e., substrate) by moving the tip of the cantileverto a position adjacent to the atom or molecule to be moved andsubsequently increasing the attraction between the tip and the atom ormolecule by moving the tip closer to the surface. Then, while the atomor molecule remains bound to the tip and to the surface of thesubstrate, the tip is moved laterally to drag the atom or molecule to adesired position on the substrate surface. The tip can then be movedaway from the surface, reducing the attraction between the atom ormolecule and tip, and leaving the atom or molecule bound at the desiredposition. Methods of generating data structures using cantilevers aredescribed in U.S. Pat. No. 6,236,589, for example. By using an array ofhigh performance cantilevers, very high density structures can befabricated.

It should be obvious to those of skill in the art that the methodsdescribed above are non-limiting and that the cantilevers according tothe invention can be used in any methods relying on cantilevers whichare know in the art or which may be designed in the future and that suchmethods are encompassed within the scope of the instant invention.

EXAMPLES

The invention will now be further illustrated with reference to thefollowing examples. It will be appreciated that what follows is by wayof example only and that modifications to detail may be made while stillfalling within the scope of the invention.

Example 1 FIB Generated Cantilever

To make rectangular cantilevers, a starting material comprising astraight beam-shaped B Microlever with a nominal resonant frequency of15 kHz in air and a nominal force constant of 0.02 N/m. After milling,the resonant frequency of one of the cantilevers provided in this way(cantilever 1) in air increased to 126 kHz, and in water the resonantfrequency increased from 3.5 kHz to 51 kHz (Table 2). In both cases,there is a peak centered at zero frequency due to 1/f and otherelectronic noise. The force constant increased to 0.20 N/m.

The resonant frequency of a cantilever 2 produced by this method wasincreased by a similar amount, i.e., to 106 kHz in air and 42 kHz inwater. The small difference between cantilevers 1 and 2 is probably dueto the slightly longer legs of cantilever 2. Note that the ratioω_(s)/ω_(v) improved in the modified cantilevers, and is ˜0.4 comparedwith 0.25-0.3 for unmodified cantilevers.

To make a V-shaped cantilever (cantilevers 3-5), a starting material wasselected which was a V-shaped F Microlever, with a nominal resonantfrequency of 120 kHz in air and a nominal force constant of 0.5 N/m.After milling, the resonant frequency of a cantilever 4 produced in thisway in air remained nearly unchanged (123 kHz). However, the resonantfrequency in water increased to 54 kHz, while the force constantdecreased to 0.30 N/m. Here ω_(s)/ω_(v), improved to 0.44. Similarresults were obtained for cantilevers 3 and 5.

The deflection due to thermal fluctuations of modified cantilevers inwater to that of unmodified cantilevers with similar spring constantswas compared. The reduced dimensions of the cantilevers led to improvednoise characteristics. Over a bandwidth of 100 Hz-10 kHz, the thermalnoise was lower for cantilever 1 than for a conventional E Microlever(FIGS. 2H-I). The RMS thermal deflection of cantilever 1 in thisbandwidth was 0.032 nm, while the RMS deflection of the E cantilever was0.22 nm. Since the total thermal noise of a cantilever scales ask^(−1/2), part of the decrease in thermal noise comes from the higherspring constant of cantilever 1 (0.20 N/m, as compared to 0.11 for the Ecantilever). However, this leads to an expected reduction to 74% of thehigher value. Most of the reduction in noise over this bandwidth is dueto increased resonant frequency. The RMS deflection over this bandwidthis similar to that of a conventional F Microlever (0.029 nm). The FMicrolever has a nominal spring constant of 0.5 N/m, more than twicethat of cantilever 1.

In one aspect, a rectangular cantilever (FIG. 2D) was milled from asimple beam-shaped cantilever with a length of 200 μm, a width of 20 μm,and a nominal thickness of 0.6 μm (the B-type Microlever). The lengthwas truncated to 35 μm. The beam-shaped cantilever was then milled toform a square at the base, leaving two legs of approximately 0.75 μm inwidth and 20 μm in length. A 15 μm×20 μm rectangular pad was left at theend of the legs in order to reflect the laser beam onto the photodiode.Note that this cantilever has no tip, although one could readily beadded by electron beam deposition.

A V-shaped cantilever (FIG. 2E) was made by starting with a commercialV-shaped cantilever with a length of 85 μm from base to free end, a legwidth of 18 μm, and a nominal thickness of 0.6 μm (the F-typeMicrolever). This was modified to produce two legs that wereapproximately 1 μm wide and 20 μm long, leaving the tip and a sufficientsurface area for an optical lever at the free end (FIG. 2E). Largeportions of the original legs were left in place, so that the finalcantilever was a compound structure.

Generally, before milling, the cantilevers were sputter-coated with ˜3nm of chromium to eliminate charging effects, then mounted to aluminumstubs with conductive silver paint. The milling was performed in an FEIFIB-200/xp focused ion beam workstation with a 30 kV Ga⁺ ion beam, and abeam current of 150 pA (FEI, Hillsboro, Oreg.).

Several cantilevers of each type were milled, and the resonant frequencyin air and fluid, as well as the thermal noise characteristics, of eachcantilever was determined (see, Table 2). The cantilevers were mountedin a standard ambient or fluid tapping cell. Measurements were performedusing a Multimode AFM with a Nanoscope IIIa controller equipped with aSignal Access Module (Digital Instruments, Santa Barbara, Calif.).Cantilever deflection voltages were collected with a custom dataacquisition system, and the data analyzed using custom software writtenin Interactive Data Language (Research Systems, Inc., Boulder, Colo.)(see, e.g., Heinz, et al., 2000, J. Phys. Chem. B. 104: 622).

To determine the resonant frequency, the raw cantilever deflectionsignal was sampled at 1 MHz, high-pass filtered above 100 Hz to removelow frequency electronic noise, and used to calculate the power spectraldensity. Resonant frequency was also measured with the DigitalInstruments frequency tuning software, and checked to ensure that it wasconsistent with the previous result.

Thermal noise was tested in a similar fashion. The raw deflection signalof a free cantilever in pure water was bandpass filtered from 100 Hz to10 kHz, and the root mean square (RMS) deflection was calculated. Forseveral of the cantilevers, the force constant was also measured usingan independently calibrated reference cantilever (CLFC-NOBO;ThermoMicroscopes) (see, Gibson, et al., 1996, Nanotechnology 7: 259(1996).

A summary of the properties of the cantilevers so produced is shown inTable 2 below.

TABLE 2 Properties of Cantilevers* k F₀ air F₀ fluid RMS NoiseCantilever Type (N/m) (kHz) (kHz) (nm) 1 rectangular 0.20* 127 50.60.032 2 rectangular N/D 106 42.4 0.036 3 V-shaped N/D 136 62.5 0.067 4V-shaped 0.30* 123 53.9 0.032 5 V-shaped N/D 123 53.0 N/D E V-shaped0.11** 35.9 7.8 0.220 F V-shaped 0.5^(#) 122 38.0 0.029 *Summary offorce constant (k), resonant frequency in air and fluid (F₀), and RMSnoise deflection from 100 Hz-10 kHz in pure water for 5 modifiedcantilevers and 2 conventional cantilevers (E and F Microlevers,ThermoMicroscopes). **Tested using reference spring method. # Nominalforce constant reported by manufacturer. N/D: Not determined.

Example 2 Generation of Cantilevers by Electron Beam Deposition

High performance cantilevers were grown on the end of conventionalsilicon nitride cantilevers or near the apex of high force constantSi-cantilevers. The silicon nitride cantilevers were V-shaped and 83 μmfrom based to free end, with a nominal force constant of 0.5 N/m. TheSi-cantilevers were straight beams 125 um long with a force constant of10-50 N/m. The cantilevers were mounted on a standard scanning electronmicroscope (SEM) mount, with the cantilever pointing toward the electronbeam. An Amray 1810 SEMI equipped with a tungsten filament source wasused. The microscope was operated at 30 kV using a condenser lenssetting of 14, at 40,000 to 60,000× magnification and working distanceof ˜10 mm.

Electron beam deposited cantilevers up to 12 μm in length wereconstructed, with the only obvious limit being patience of the SEMoperator (FIG. 1A). On a standard SEM, the mechanical drift in thesystem required adjustment of the beam every 1-5 minutes, over the timecourse of 3-5 hours for a 10 μm cantilever. Further, the growth of thecantilever required frequent refocusing to maintain a small spot at thegrowing end of the cantilever. The cantilevers generated by this methodhad a somewhat irregular tapered shape, with a diameter at the basetypically less than 1 um and a diameter at the free end of 100-300 nm.

Other variants of this type of cantilever included constructing verysmall cantilevers near the apex of the tip of a Si-cantilever (FIG. 1B)and the addition (by electron beam deposition) of a pad in the middle ofthe cantilever (FIG. 1C). The high performance cantilevers were producedfrom this starting material using the smallest and most well-focusedelectron beam possible. The tapered structure is inadvertent and mayresults from surface diffusion of activated molecules out of theirradiation volume, or from out of focus electron irradiation along thelength structure; however, it does not significantly impact theperformance properties of the cantilever.

Variations, modifications, and other implementations of what isdescribed herein will occur to those of ordinary skill in the artwithout departing from the spirit and scope of the invention.

All patents, patent applications, and references cited herein areincorporated in their entireties herein.

1. A cantilever for use in a scanning probe microscope comprising awidth to thickness ratio of about 3:1 or less and which is smaller in atleast one dimension than about 5 μm, and wherein the cantilevercomprises a spring constant between 1×10⁻⁶ and 0.1 N/m.
 2. Thecantilever according to claim 1, wherein the cantilever has a resonantfrequency equal to or above 10 kHz.
 3. The cantilever according to claim1, wherein the cantilever has a resonant frequency equal to or above 100kHz.
 4. The cantilever according to claim 1 wherein the cantilevercomprises silicon, silicon nitride, silicon dioxide, a metal, a plastic,and a silicon-based rubber.
 5. The cantilever according to claim 4,wherein the metal is selected from gold, aluminum, silver and nickel. 6.The cantilever according to claim 4, wherein the silicon-based rubber isPDMS.
 7. The cantilever according to claim 1, wherein the cantilevercomprises a reflective portion and/or comprises a conductive material.8. The cantilever according to claim 1, wherein the cantilever comprisesa width to thickness ratio of about 1:1 or less.
 9. A method formeasuring a property of a sample, comprising: detecting an interactionbetween a cantilever according to claim 1 and the sample, wherein theinteraction provides a measure of the property of the sample.
 10. Themethod according to claim 9, wherein the property comprises one or moresurface features of the molecule.
 11. The method according to claim 9,wherein the cantilever further comprises one or more biologicalmolecules and wherein the one or more biological molecules interact withone or more molecules of the sample.
 12. The method according to claim11, wherein the biological molecule binds to the one or more molecules.13. The method according to claim 11, wherein the one or more biologicalmolecules is selected from the group consisting of: nucleic acids,proteins, polypeptides, peptides, receptors, ligands, enzymes, antigens,drug molecules, therapeutic agents, lipids, lipid bilayers, detergents,a cell membrane fraction, organelles, and zwitterions.
 14. The methodaccording to claim 11, wherein the nucleic acid is selected from thegroup consisting of: a DNA molecule, RNA molecule, antisense molecule,ribozyme, triple helix forming molecule, an aptamer; and combinationsand modified forms thereof.
 15. The method according to claim 14,wherein the sample comprises one or more a cell, nucleic acids,proteins, polypeptides, peptides, receptors, ligands, enzymes, antigens,drug molecules, therapeutic agents, lipids, a cell membrane fraction,organelles, and microorganisms.
 16. The method according to claim 14,wherein the property of the sample comprises one or more of: surfacetopography, binding, a chemical reaction, a cellular response, orpolymerization.
 17. A cantilever for use in a scanning probe microscopeaccording to claim 1, wherein the width to thickness ratio reducesdamping of the cantiler's resonant frequency.
 18. A method for producinga cantilever comprising: (a) providing a starting material; (b) exposingthe starting material to an ion beam; and (c) removing molecules fromthe starting material to generate a cantilever which has a width tothickness ratio of about 3:1 or less, and which is smaller in at leastone dimension than about 5 μm, and wherein the cantilever comprises aspring constant between 1×10⁻⁶ and 0.1 N/m.
 19. The method according toclaim 18, further comprising imaging the starting material at one ormore time intervals.
 20. The method according to claim 18, wherein thestarting material comprises silicon, silicon nitride, silicon dioxide,or a metal.
 21. The method according to claim 18, wherein the cantilevercomprises a resonant frequency above at least about 10 kHz.
 22. Themethod according to claim 18, wherein the cantilever comprises aresonant frequency above at least about 100 kHz.
 23. The methodaccording to claim 18, wherein the starting material is a beam, a film,a sheet, a V-shaped material, or a rectangular shaped material.
 24. Themethod according to claim 18, wherein the starting material is acantilever.
 25. The method according to claim 18, further comprising astep of generating a tip at an end of the cantilever.
 26. The methodaccording to claim 18, wherein the tip is generated by electron beamdeposition.
 27. The method according to claim 18, wherein the cantilevercomprises a reflective surface.
 28. The method according to claim 18,wherein the starting material is a conductive material.
 29. A cantileverfor use in a scanning probe microscope comprising a width to thicknessratio of about 3:1 or less and which is smaller in at least onedimension than about 5 μm and which is larger in at least one dimensionthan about 20 nm, and wherein the cantilever comprises spring constantbetween 1×10⁻⁶ and 0.1 N/m.